Best Known (71, 71+14, s)-Nets in Base 9
(71, 71+14, 683282)-Net over F9 — Constructive and digital
Digital (71, 85, 683282)-net over F9, using
- net defined by OOA [i] based on linear OOA(985, 683282, F9, 14, 14) (dual of [(683282, 14), 9565863, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(985, 4782974, F9, 14) (dual of [4782974, 4782889, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(985, 4782976, F9, 14) (dual of [4782976, 4782891, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(985, 4782976, F9, 14) (dual of [4782976, 4782891, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(985, 4782974, F9, 14) (dual of [4782974, 4782889, 15]-code), using
(71, 71+14, 3162045)-Net over F9 — Digital
Digital (71, 85, 3162045)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(985, 3162045, F9, 14) (dual of [3162045, 3161960, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using
(71, 71+14, large)-Net in Base 9 — Upper bound on s
There is no (71, 85, large)-net in base 9, because
- 12 times m-reduction [i] would yield (71, 73, large)-net in base 9, but